A particle of mass \(200 \,MeV / c ^{2}\) collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in \(eV\) ) is \(\frac{ N }{4} .\) The value of \(N\) is : (Given the mass of the hydrogen atom to be \(\left.1\, GeV / c ^{2}\right)\)

In a system two particles of masses \(m_1=3 \mathrm{~kg}\) and \(\mathrm{m}_2=2 \mathrm{~kg}\) are placed at certain distance from each other. The particle of mass \(m_1\) is moved towards the center of mass of the system through a distance \(2 \mathrm{~cm}\). In order to keep the center of mass of the system at the original position, the particle of mass \(\mathrm{m}_2\) should move towards the center of mass by the distance _______\(\mathrm{cm}\).

In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6\  \mathrm{MeV} /\) Nucleon dissociated into middle mass nuclides \((A \approx 118)\), having binding energy of \(8.6 \ \mathrm{MeV} / \mathrm{Nucleon}\). The energy released in the process would be \(\mathrm{MeV}\).

Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is \( T=2\pi\sqrt{\frac{R_{e}}{g}} \) (for satellite very close to the earth surface), where \( R_{e} \) radius of earth and g acceleration due to gravity.
In the light of the above statements, choose the correct answer from the options given below :

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then:

If the gravitational field in the space is given as \(\left(-\frac{ K }{ r ^2}\right)\). Taking the reference point to be at \(r =2\,cm\) with gravitational potential \(V =10\,J / kg\). Find the gravitational potential at \(r =3\,cm\) in \(SI\) unit (Given, that \(K =6\,J cm / kg\) )

In a Young’s double slit experiment the ratio of the slit’s width is \(4 : 1.\) The ratio of the intensity of maxima to minima, close to central fringe on the screen will be

This question has Statement \(-1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement \(1\) : Very large size telescopes are reflecting telescopes instead of refracting telescopes. Statement \(2\) : It is easier to provide mechanical support to large size mirrors than large size lenses.

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be \(\dots \;\)%

Match List \(I\) with List \(II\)

LIST\(-I\)	LIST\(-II\)
\((A)\) Surface tension	\((I)\) \(Kg m ^{-1} s ^{-1}\)
\((B)\) Pressure	\((II)\) \(Kg ms^{-1 }\)
\((C)\) Viscosity	\((III)\) \(Kg m ^{-1} s ^{-2}\)
\((D)\) Impulse	\((IV)\) \(Kg s ^{-2}\)

Choose the correct answer from the options given below :